Question

Aubrey and Charlie are driving to a city that is 120 miles from their house. they have already traveled 20 miles ,and they are driving at a constant rate of 50 mi /h. write a function that models the distance they drive as a function of time .what is a reasonable domain for this situation ?

Answer 1

The linear function is
`y=50x+20`

The reasonable domain is
`0\ hours \leq x\leq 2\ hours`

Explanation:

Let

x ----> the time in hours

y ---> the distance in miles

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

The slope is
`m=50\ (miles)/(hour)`

The y-intercept is
`b=20\ miles`

substitute

`y=50x+20`

Find the domain for x

For y=120 miles

Find the value of x

substitute the value of y in the linear equation and solve for x

`120=50x+20`

`50x=120-20`

`50x=100`

`x=2\ hours`

therefore

The domain is the interval [0,2]

`0\ hours \leq x\leq 2\ hours`